We note that the SSPERK\((10,4)-\tilde{b}^T_2\)  performed the worst for all problems. In all the numerical studies, this method overestimates the local error and returns a really small step-size causing the method to do an incredibly large amount of work to integrate the problem to the final time. At the final time, the global error (the precision) is much lower than the prescribed tolerance (i.e. \(1e{-12}\)  vs. \(1e{-7}\) ). A practical error estimate “ensures that the step-sizes are sufficiently large to avoid unnecessary computational work" [1]}. SSPERK\((10,4)-\tilde{b}^T_2\)  is not practical since it fails to do this.
